Abstract
The paper is concerned with combinatorial description of almost perfect nonlinear functions (APN-functions). A complete characterization of n-place APN-functions in terms of (n − 1)-place subfunctions is obtained. An n-place function is shown to be an APN-function if and only if each of its (n − 1)-place subfunctions is either an APN-function or has the differential uniformity 4 and the admissibility conditions hold. A detailed characterization of 2, 3 or 4-place APN-functions is presented.
Originally published in Diskretnaya Matematika (2015) 27, №3, 3-16 (in Russian).
Funding source: Russian Foundation for Basic Research
Award Identifier / Grant number: 15-07-01328
Funding statement: This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 15-07-01328) and the Programme of Support of Leading Scientific Schools of the President of the Russian Federation (grant no. NSh-1939.2014.1)
Acknowledgement
The author expresses her gratitude to I.,A. Kruglikov for his attentive reading of the manuscript and valuable advice.
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Articles in the same Issue
- Frontmatter
- Research Article
- Characterization of almost perfect nonlinear functions in terms of subfunctions
- Research Article
- Estimates for distribution of the minimal distance of a random linear code
- Research Article
- The distributions of interrecord fillings
- Research Article
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- Overgroups of order 2n additive regular groups of a residue ring and of a vector space